Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in JAVA):

Solution:
import java .io.*; 
import java.util.*;
import java.lang.*;
import java.util.Arrays; 
public class RATHOD 
{ 
    public static void main (String[] args) 
    { 
    Scanner sc=new Scanner(System.in);
    long n=sc.nextLong();
    n=2*(4*n+1);
    long i=2;
    long pf=0;
    int flag=0;
    long power=0;
     HashMap<Long, 
            Integer> s = new HashMap<Long, 
                                     Integer>(); 
    for(i=3;i<=Math.sqrt(n);i=i+2)
    {
        power=0;
        s.put(i * i, 1); 
        if(s.containsKey(n - i * i))
        { 
            flag=1;
            break;
        } 
    }
    if(flag==0)
    System.out.println("NO");
    else
    {
    System.out.println("YES");
    }
   
    
    } 
}